660 Mr. W. Sutherland on the Electri 



ic 



of electron pairs is excluded by the law of the inverse fourth 

 power for molecular attraction. I think that this result 

 about the inverse seventh power is erroneous because the 

 writer uses in Boltzmann's law the potential energy of a pair 

 of molecules instead of the mean potential energy of all the 

 molecules, which is the main object of investigation. More- 

 over, in this case Boltzmann's law is made to give a relation 

 between the coordinates of the two molecules, which co- 

 ordinates cease to be independent variables. For these 

 reasons I believe Boltzmann's law is made to yield a result 

 which is not correct. Moreover, in the treatment of the 

 problem no account is taken of the principle that attractive 

 forces preponderate because by their own action they increase 

 themselves, while repulsive forces diminish themselves. As a 

 large mass of experimental evidence now furnishes cumulative 

 support to the theory of the electric origin of molecular attrac- 

 tion, I shall not attempt to discuss the analysis of van der Waals, 

 Jr., in detail, as it seems to me that the question raised by him 

 is rather that of the correct use of the Boltzmann-Gribbs theorem 

 than that of the origin of molecular attraction. 



The ideally simplest case in which molecular force can be 

 investigated is at the absolute zero of temperature, at which 

 the kinetics of molecules disappear, leaving the statics for 

 unencumbered study. In "A Kinetic Theory of Solids" 

 (Phil. Mag. [5] xxxii.) it was shown that the rigidity of 

 metals at absolute zero could be found with considerable 

 accuracy by a safe extrapolation from experimental data. 

 Then it was further shown in " The Electric Origin of 

 Rigidity and Consequences " (Phil. Mag. [6] vii.) that at 

 absolute zero the rigidity of a collection of electrically 

 polarized molecules is equal to their electrostatic energy per 

 unit volume. If we imagine the electric polarization to 

 consist in each molecule's having an electron pair \) J whose 

 charges are e at distance (m/p ) 1 /' 3 apart, m being the mass 

 of the molecule and p the density of the metal, with K for its 

 dielectric capacity and N for the rigidity at absolute {zero, 

 then this result is given by the formula 

 _ 2tt (m/ Po ) 23 



1N -3K (m/pj>> W 



which was found to express the experimentally derived facts 

 satisfactorily. This is simply Maxwell's expression 2ttD 2 /K 

 for the energy in a dielectric associated with an electric dis- 

 placement D, for, when we consider the electric displacement 

 per unit area corresponding with e per molecule, we get 

 e/(m/p ) 2 ^ to be used instead of D, the result being divided 

 by 3 for statistical reasons. 



But we must look more closely into the differences between 



